There is no minimum seal thickness for a rigid tray in the industry.  The minimum thickness required is whatever is needed to achieve and maintain your desired strength and integrity criteria for your packaging.

It sounds like what you are describing are the veins that can be found in the Tyvek. Tyvek is produced by DuPont in its flash-spinning and bonding process, in which HDPE fibers are flashspun and laid onto a web. These fibers are layered and create the Tyvek structure. It is this “crossing” of the fibers that create the “tortuous path” (per DuPont) and prevents the microorganisms from getting through the Tyvek, helping create the sterile barrier.

If you hold the Tyvek up to the light you can see these fibers within the lid. In most cases, they are small in diameter, and on occasion there are larger fibers. The process of flash-spinning does create a thickness range within the Tyvek structure; the range for Tyvek 1073B is from 3.5 mils to 11.1 mils (per DuPont). To compensate for such variation, converters typically utilize an air knife coating of up to 7 mils thick.

It is possible that this large vein impacted how the adhesive was applied to the Tyvek. However, I would advise you to contact your lid supplier to get some feedback from them regarding this issue. They should be able to advise you on what rejection rate you should expect to see and help you develop inspection protocols.